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In this exercise we consider matching problems where some

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 36E Chapter 3.SE

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 36E

In this exercise we consider matching problems where some man-woman pairs are not allowed.a) Extend the definition of a stable matching to cover the situation where there are the same number of men and women, but certain pairs of men and women are forbidden. Avoid all cases where a man and a woman would prefer each other to their current situation, including those involving unmatched people.________________b) Adapt the deferred acceptance algorithm to find stable matchings when there are the same number of men and women, but certain man-woman pairs are forbidden. Be sure to consider people who are unmatched at the end of the algorithm. (Assume that an unmatched person prefers a match with a member of the opposite gender who is not a forbidden partner to remaining unmatched.)________________c Prove that all matchings produced by the algorithm from (b) arc stable, according to the definition in part (a).

Step-by-Step Solution:

SOLUTIONStep 1In this problem, we are asked to consider the matching problems where some man woman pair is forbidden and then do the following .

Step 2 of 4

Chapter 3.SE, Problem 36E is Solved
Step 3 of 4

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

The full step-by-step solution to problem: 36E from chapter: 3.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 36E from 3.SE chapter was answered, more than 262 students have viewed the full step-by-step answer. The answer to “In this exercise we consider matching problems where some man-woman pairs are not allowed.a) Extend the definition of a stable matching to cover the situation where there are the same number of men and women, but certain pairs of men and women are forbidden. Avoid all cases where a man and a woman would prefer each other to their current situation, including those involving unmatched people.________________b) Adapt the deferred acceptance algorithm to find stable matchings when there are the same number of men and women, but certain man-woman pairs are forbidden. Be sure to consider people who are unmatched at the end of the algorithm. (Assume that an unmatched person prefers a match with a member of the opposite gender who is not a forbidden partner to remaining unmatched.)________________c Prove that all matchings produced by the algorithm from (b) arc stable, according to the definition in part (a).” is broken down into a number of easy to follow steps, and 148 words. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This full solution covers the following key subjects: unmatched, Women, Where, Algorithm, woman. This expansive textbook survival guide covers 101 chapters, and 4221 solutions.

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In this exercise we consider matching problems where some